Identifier
Values
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>1 [.,[.,.]]=>[2,1]=>2 [[.,.],.]=>[1,2]=>1 [.,[.,[.,.]]]=>[3,2,1]=>3 [.,[[.,.],.]]=>[2,3,1]=>2 [[.,.],[.,.]]=>[1,3,2]=>1 [[.,[.,.]],.]=>[2,1,3]=>2 [[[.,.],.],.]=>[1,2,3]=>1 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>4 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>3 [.,[[.,.],[.,.]]]=>[2,4,3,1]=>2 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>3 [.,[[[.,.],.],.]]=>[2,3,4,1]=>2 [[.,.],[.,[.,.]]]=>[1,4,3,2]=>1 [[.,.],[[.,.],.]]=>[1,3,4,2]=>1 [[.,[.,.]],[.,.]]=>[2,1,4,3]=>2 [[[.,.],.],[.,.]]=>[1,2,4,3]=>1 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>3 [[.,[[.,.],.]],.]=>[2,3,1,4]=>2 [[[.,.],[.,.]],.]=>[1,3,2,4]=>1 [[[.,[.,.]],.],.]=>[2,1,3,4]=>2 [[[[.,.],.],.],.]=>[1,2,3,4]=>1 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>5 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>4 [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>3 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>4 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>3 [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>2 [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>2 [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>3 [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>2 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>4 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>3 [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>2 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>3 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>2 [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>1 [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>1 [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>1 [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>1 [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>1 [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>2 [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>2 [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>1 [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>1 [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>3 [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>2 [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>1 [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>2 [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>1 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>4 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>3 [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>2 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>3 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>2 [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>1 [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>1 [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>2 [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>1 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>3 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>2 [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>1 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>2 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>1 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>6 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>5 [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>4 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>5 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>4 [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>3 [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>3 [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>4 [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>3 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>5 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>4 [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>3 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>4 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>3 [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>2 [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>2 [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>2 [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>2 [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>2 [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>3 [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>3 [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>2 [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>2 [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>4 [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>3 [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>2 [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>3 [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>2 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>5 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>4 [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>3 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>4 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>3 [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>2 [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>2 [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>3 [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>2 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>4 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>3 [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>2 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>3 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>2 [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>1 [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>1 [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>1 [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>1 [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>1 [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>1 [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>1 [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>1 [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>1 [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>1 [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>1 [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>1 [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>1 [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>1 [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>2 [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>2 [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>2 [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>2 [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>2 [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>1 [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>1 [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>1 [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>1 [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>1 [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>3 [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>3 [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>2 [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>2 [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>1 [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>1 [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>2 [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>2 [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>1 [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>1 [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>4 [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>3 [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>2 [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>3 [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>2 [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>1 [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>1 [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>2 [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>1 [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>3 [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>2 [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>1 [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>2 [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>1 [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>5 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>4 [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>3 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>4 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>3 [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>2 [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>2 [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>3 [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>2 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>4 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>3 [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>2 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>3 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>2 [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>1 [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>1 [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>1 [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>1 [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>1 [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>2 [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>2 [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>1 [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>1 [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>3 [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>2 [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>1 [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>2 [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>1 [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>4 [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>3 [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>2 [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>3 [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>2 [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>1 [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>1 [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>2 [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>1 [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>3 [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>2 [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>1 [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>2 [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>1 [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>7 [.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>3 [.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>4 [.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>3 [.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>4 [.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>3 [.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>3 [.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>2 [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>1 [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>1 [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>1 [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>1 [[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>1 [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>1 [[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>1 [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>1 [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>1 [[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>1 [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>1 [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>1 [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>2 [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>5 [[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>2 [[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>2 [[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>1 [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>6 [[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>5 [[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>4 [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>5 [[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>4 [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>3 [[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>3 [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>4 [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>5 [[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>4 [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>2 [[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>5 [[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>2 [[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>1 [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>5 [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>2 [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>4 [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>2 [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>3 [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>2 [[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>1 [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>2 [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>1 [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>8 [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>7 [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>6 [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>7 [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>6 [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>3 [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>4 [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>2 [.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>2 [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>3 [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>7 [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>6 [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>6 [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>5 [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>4 [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>3 [.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>4 [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>3 [.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>3 [.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>4 [.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>3 [.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>3 [.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>2 [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>1 [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>1 [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>1 [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>1 [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>1 [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>1 [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>1 [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>1 [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>1 [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>1 [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>1 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>2 [[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>2 [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>2 [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>1 [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>3 [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>3 [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>1 [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>4 [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>3 [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>2 [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>2 [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>3 [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>3 [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>2 [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>2 [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>2 [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>2 [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>5 [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>3 [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>3 [[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>2 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>6 [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>4 [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>3 [[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>2 [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>2 [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>2 [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>2 [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>4 [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>2 [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>3 [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>2 [[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>2 [[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>1 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>7 [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>6 [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>5 [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>6 [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>5 [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>4 [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>6 [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>3 [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>5 [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>3 [[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>2 [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>1 [[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>1 [[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>1 [[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>1 [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>1 [[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>1 [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>6 [[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>2 [[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>1 [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>5 [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>2 [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>1 [[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>1 [[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>4 [[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>3 [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>1 [[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>2 [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>1 [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>9 [.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>2 [[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>1 [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>10 [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>2 [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>1 [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>8 [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>9 [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>2 [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>2 [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>1 [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>1 [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>3 [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>1 [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>3 [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>3 [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>2 [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>1 [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>7 [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,8,9,7,6,5,4,3,2]=>1 [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>1 [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>10 [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>8 [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>7 [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,8,7,9,6,5,4,3,2]=>1 [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[1,9,10,8,7,6,5,4,3,2]=>1 [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>1 [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]=>2 [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]=>4 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[6,5,4,3,2,1,10,9,8,7]=>6 [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]=>8 [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>7 [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>6 [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>5 [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>4 [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>3 [[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>2 [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>8 [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>7 [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>6 [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>5 [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>4 [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>3 [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>2 [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>2 [[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>2 [[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>2 [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>2
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The first entry of the permutation.
This can be described as 1 plus the number of occurrences of the vincular pattern ([2,1], {(0,0),(0,1),(0,2)}), i.e., the first column is shaded, see [1].
This statistic is related to the number of deficiencies St000703The number of deficiencies of a permutation. as follows: consider the arc diagram of a permutation $\pi$ of $n$, together with its rotations, obtained by conjugating with the long cycle $(1,\dots,n)$. Drawing the labels $1$ to $n$ in this order on a circle, and the arcs $(i, \pi(i))$ as straight lines, the rotation of $\pi$ is obtained by replacing each number $i$ by $(i\bmod n) +1$. Then, $\pi(1)-1$ is the number of rotations of $\pi$ where the arc $(1, \pi(1))$ is a deficiency. In particular, if $O(\pi)$ is the orbit of rotations of $\pi$, then the number of deficiencies of $\pi$ equals
$$ \frac{1}{|O(\pi)|}\sum_{\sigma\in O(\pi)} (\sigma(1)-1). $$
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.